Oscillation-Driven Reservoir Computing for Long-Term Replication of Chaotic Time Series

Reservoir computing, a type of recurrent neural networks, has recently been exploited for the model-free prediction of the temporal evolution of various chaotic dynamical systems. However, the prediction horizon is limited owing to the instability of the reservoir-computing system. In this study, to suppress this instability, oscillations were fed into the reservoir network, which exhibited chaotic behavior. In response to oscillations, the reservoir network generates complex and stable dynamics, allowing it to replicate long-term chaotic time-series data. While the weights of the oscillation inputs and the weights within the reservoir were fixed, only the readout weights were trained using recursive least squares. We call this the oscillation-driven reservoir computing (ODRC) and applied it to reproduce the time series obtained using the Lorenz system. Our results indicate that the ODRC successfully replicates the time series better than conventional methods while maintaining a low computational cost.